Spin and valley noise in two-dimensional Dirac materials

Physical Review Letters

Volumn 113, Issue 4, 2014, Pages

  Tse, Wang Kong ^a   Saxena, A ^a   Smith, D L ^a   Sinitsyn, N A ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LANDFORMS;

DICHALCOGENIDES; INTERVALLEY SCATTERING; NOISE POWER SPECTRUM; NOISE SPECTROSCOPY; OPTICAL FARADAY ROTATIONS; RELAXATION DYNAMICS; SPIN NOISE;

SPIN FLUCTUATIONS;

EID: 84905043761     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.113.046602     Document Type: Article

References (36)

1. For a recent review see, for example, T.O. Wehling, A.M. Black-Schaffer, and A.V. Balatsky, arXiv:1405.5774v1 [Adv. Phys. (to be published)].
2. C. Jin, F. Lin, K. Suenaga, and S. Iijima, Phys. Rev. Lett. 102, 195505 (2009); PRLTAO 0031-9007 10.1103/PhysRevLett.102.195505
3. N. Alem, R. Erni, C. Kisielowski, M.D. Rossell, W. Gannett, and A. Zettl, Phys. Rev. B 80, 155425 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.155425
4. K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, and A.K. Geim, Proc. Natl. Acad. Sci. U.S.A. 102, 10451 (2005); PNASA6 0027-8424 10.1073/pnas.0502848102 (Pubitemid 41061574)
5. K.F. Mak, C. Lee, J. Hone, J. Shan, and T.F. Heinz, Phys. Rev. Lett. 105, 136805 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.105.136805
6. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, and F. Wang, Nano Lett. 10, 1271 (2010). NALEFD 1530-6984 10.1021/nl903868w
7. Q.H. Wang, K. Kalantar-Zadeh, A. Kis, J.N. Coleman, and M.S. Strano, Nat. Nanotechnol. 7, 699 (2012). NNAABX 1748-3387 10.1038/nnano.2012.193
8. C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 (Pubitemid 41776999)
9. T. Cao, J. Feng, J. Shi, Q. Niu, and E. Wang, Nat. Commun. 3, 887 (2012). NCAOBW 2041-1723 10.1038/ncomms1882
10. H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Nat. Nanotechnol. 7, 490 (2012). NNAABX 1748-3387 10.1038/nnano.2012.95
11. K.F. Mak, K. He, C. Lee, G.H. Lee, J. Hone, T.F. Heinz, and J. Shan, Nat. Mater. 12 207 (2013); NMAACR 1476-1122 10.1038/nmat3505
12. H. Shi, R. Yan, S. Bertolazzi, J. Brivio, B. Gao, A. Kis, D. Jena, H. G. Xing, and L. Huang, ACS Nano 7, 1072 (2013); ANCAC3 1936-0851 10.1021/nn303973r
13. D. Lagarde, L. Bouet, X. Marie, C.R. Zhu, B.L. Liu, T. Amand, P.H. Tan, and B. Urbaszek, Phys. Rev. Lett. 112, 047401 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.047401
14. For recent reviews, see V.S. Zapasskii, Adv. Opt. Photonics 5, 131 (2013); AOPAC7 1943-8206 10.1364/AOP.5.000131
15. G.M. Müller, M. Oestreich, M. Römer, and J. Hübner, Physica (Amsterdam) 43E, 569 (2010). PELNFM 1386-9477 10.1016/j.physe.2010.08. 010
16. S.A. Crooker, L. Cheng, and D.L. Smith, Phys. Rev. B 79, 035208 (2009); PRBMDO 1098-0121 10.1103/PhysRevB.79.035208
17. M. Oestreich, M. Romer, R.J. Haug, and D. Hägele, Phys. Rev. Lett. 95, 216603 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.216603 (Pubitemid 41777069)
18. G.M. Müller, M. Römer, D. Schuh, W. Wegscheider, J. Hübner, and M. Oestreich, Phys. Rev. Lett. 101, 206601 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.206601
19. S.V. Poltavtsev, I.I. Ryzhov, M.M. Glazov, G.G. Kozlov, V.S. Zapasskii, and A.V. Kav, Phys. Rev. B 89, 081304(R) (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.081304
20. S.A. Crooker, J. Brandt, C. Sandfort, A. Greilich, D.R. Yakovlev, D. Reuter, A.D. Wieck, and M. Bayer, Phys. Rev. Lett. 104, 036601 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.036601
21. R. Dahbashi, J. Hübner, F. Berski, K. Pierz, and M. Oestreich, Phys. Rev. Lett. 112, 156601 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.156601
22. F. Berski, H. Kuhn, J.G. Lonnemann, J. Hübner, and M. Oestreich, Phys. Rev. Lett. 111, 186602 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111. 186602
23. W.-K. Tse and A.H. MacDonald, Phys. Rev. B 84, 205327 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.205327
24. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Phys. Rev. Lett. 108, 196802 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.196802
25. See the Supplemental Material at http://link.aps.org/supplemental/10. 1103/PhysRevLett.113.046602 for a derivation of Eqs. (3) and (4) and detailed expressions of the spin noise power with its limiting behavior for slow and fast intervalley relaxation rates.
26. R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, Berlin, 2003).
27. The renormalized (Equation presented) factor has also been recently discussed in A. Kormányos, V. Zólyomi, N.D. Drummond, and G. Burkard, Phys. Rev. X 4, 011034 (2014). PRXHAE 2160-3308 10.1103/PhysRevX.4. 011034
28. F. Li, Y.V. Pershin, V.A. Slipko, and N.A. Sinitsyn, Phys. Rev. Lett. 111, 067201 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.067201
29. The small spin-orbit coupling corrections (Equation presented) to the spin and valley relaxation times are neglected in our phenomenological relaxation time approximation. We expect that such corrections change only the quantitative but not the qualitative features we find.
30. M.B. Lundeberg, R. Yang, J. Renard, and J.A. Folk, Phys. Rev. Lett. 110, 156601 (2013); PRLTAO 0031-9007 10.1103/PhysRevLett.110.156601
31. A.A. Kozikov, D.W. Horsell, E. McCann, and V.I. Fal'ko, Phys. Rev. B 86, 045436 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.045436
32. H. Ochoa and R. Roldán, Phys. Rev. B 87, 245421 (2013); PRBMDO 1098-0121 10.1103/PhysRevB.87.245421
33. L. Wang and M.W. Wu, Phys. Lett. A 378, 1336 (2014). PYLAAG 0375-9601 10.1016/j.physleta.2014.03.026
34. Possible correction from intervalley spin-flip scattering, which requires the simultaneous breakdown of time-reversal symmetry and large momentum transfer, is negligible compared to intravalley spin relaxation.
35. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin, 2004).
36. To separate the valley noise contribution from the background photon shot noise, one can measure the shot noise spectrum in the absence of the sample.